%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:12:54 AM UTC 2026
% Result : Theorem 0.25s 0.33s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 12 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 272 ( 26 ~; 23 |; 11 &; 198 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 2 con; 0-3 aty)
% Number of variables : 78 ( 30 ^; 44 !; 4 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mworld: $tType ).
thf(decl_23,type,
mrel: mworld > mworld > $o ).
thf(decl_24,type,
mactual: mworld ).
thf(decl_25,type,
mlocal: ( mworld > $o ) > $o ).
thf(decl_28,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_29,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(decl_31,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(decl_33,type,
eiw_di: $i > mworld > $o ).
thf(decl_34,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_35,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(decl_36,type,
big_q: $i > mworld > $o ).
thf(decl_37,type,
big_p: $i > mworld > $o ).
thf(decl_38,type,
esk1_1: mworld > $i ).
thf(decl_39,type,
esk2_1: $i > mworld ).
thf(decl_40,type,
esk3_1: $i > $i ).
thf(decl_41,type,
esk4_1: $i > mworld ).
thf(decl_42,type,
esk5_1: $i > mworld ).
thf(decl_43,type,
esk6_1: $i > mworld ).
thf(x2137,conjecture,
( mlocal
@ ( mexists_di
@ ^ [X6: $i] :
( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_p @ X6 ) ) @ ( mor @ ( mbox @ ( big_q @ X6 ) ) @ ( mbox @ ( big_p @ X9 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',x2137) ).
thf(mlocal_def,axiom,
( mlocal
= ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mlocal_def) ).
thf(mor_def,axiom,
( mor
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
| ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mor_def) ).
thf(mimplies_def,axiom,
( mimplies
= ( ^ [X2: mworld > $o,X4: mworld > $o,X3: mworld] :
( ( X2 @ X3 )
=> ( X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mimplies_def) ).
thf(mbox_def,axiom,
( mbox
= ( ^ [X1: mworld > $o,X3: mworld] :
! [X5: mworld] :
( ( mrel @ X3 @ X5 )
=> ( X1 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mbox_def) ).
thf(mforall_di_def,axiom,
( mforall_di
= ( ^ [X7: $i > mworld > $o,X3: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X3 )
=> ( X7 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mforall_di_def) ).
thf(mexists_di_def,axiom,
( mexists_di
= ( ^ [X8: $i > mworld > $o,X3: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ X3 )
& ( X8 @ X6 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mexists_di_def) ).
thf(eiw_di_cumul,axiom,
! [X3: mworld,X5: mworld,X6: $i] :
( ( ( eiw_di @ X6 @ X3 )
& ( mrel @ X3 @ X5 ) )
=> ( eiw_di @ X6 @ X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',eiw_di_cumul) ).
thf(mrel_universal,axiom,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',mrel_universal) ).
thf(eiw_di_nonempty,axiom,
! [X3: mworld] :
? [X6: $i] : ( eiw_di @ X6 @ X3 ),
file('/export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p',eiw_di_nonempty) ).
thf(c_0_10,negated_conjecture,
~ ( mlocal
@ ( mexists_di
@ ^ [X6: $i] :
( mbox
@ ( mforall_di
@ ^ [X9: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_p @ X6 ) ) @ ( mor @ ( mbox @ ( big_q @ X6 ) ) @ ( mbox @ ( big_p @ X9 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[x2137]) ).
thf(c_0_11,plain,
( mlocal
= ( ^ [Z0: mworld > $o] : ( Z0 @ mactual ) ) ),
inference(fof_simplification,[status(thm)],[mlocal_def]) ).
thf(c_0_12,plain,
( mor
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor_def]) ).
thf(c_0_13,plain,
( mimplies
= ( ^ [Z0: mworld > $o,Z1: mworld > $o,Z2: mworld] :
( ( Z0 @ Z2 )
=> ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies_def]) ).
thf(c_0_14,plain,
( mbox
= ( ^ [Z0: mworld > $o,Z1: mworld] :
! [X5: mworld] :
( ( mrel @ Z1 @ X5 )
=> ( Z0 @ X5 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_def]) ).
thf(c_0_15,plain,
( mforall_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
=> ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_di_def]) ).
thf(c_0_16,plain,
( mexists_di
= ( ^ [Z0: $i > mworld > $o,Z1: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ Z1 )
& ( Z0 @ X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mexists_di_def]) ).
thf(c_0_17,negated_conjecture,
~ ? [X23: $i] :
( ( eiw_di @ X23 @ mactual )
& ! [X22: mworld] :
( ( mrel @ mactual @ X22 )
=> ! [X21: $i] :
( ( eiw_di @ X21 @ X22 )
=> ! [X20: mworld] :
( ( mrel @ X22 @ X20 )
=> ( ! [X17: mworld] :
( ( mrel @ X20 @ X17 )
=> ( big_p @ X23 @ X17 ) )
=> ( ! [X18: mworld] :
( ( mrel @ X20 @ X18 )
=> ( big_q @ X23 @ X18 ) )
| ! [X19: mworld] :
( ( mrel @ X20 @ X19 )
=> ( big_p @ X21 @ X19 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10]),c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_18,plain,
! [X28: mworld,X29: mworld,X30: $i] :
( ~ ( eiw_di @ X30 @ X28 )
| ~ ( mrel @ X28 @ X29 )
| ( eiw_di @ X30 @ X29 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[eiw_di_cumul])])]) ).
thf(c_0_19,plain,
! [X24: mworld,X25: mworld] : ( mrel @ X24 @ X25 ),
inference(variable_rename,[status(thm)],[mrel_universal]) ).
thf(c_0_20,negated_conjecture,
! [X31: $i,X35: mworld] :
( ( ( mrel @ mactual @ ( esk2_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ( eiw_di @ ( esk3_1 @ X31 ) @ ( esk2_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ( mrel @ ( esk2_1 @ X31 ) @ ( esk4_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ~ ( mrel @ ( esk4_1 @ X31 ) @ X35 )
| ( big_p @ X31 @ X35 )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ( mrel @ ( esk4_1 @ X31 ) @ ( esk5_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ~ ( big_q @ X31 @ ( esk5_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ( mrel @ ( esk4_1 @ X31 ) @ ( esk6_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) )
& ( ~ ( big_p @ ( esk3_1 @ X31 ) @ ( esk6_1 @ X31 ) )
| ~ ( eiw_di @ X31 @ mactual ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])]) ).
thf(c_0_21,plain,
! [X3: mworld,X6: $i,X5: mworld] :
( ( eiw_di @ X6 @ X5 )
| ~ ( eiw_di @ X6 @ X3 )
| ~ ( mrel @ X3 @ X5 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_22,plain,
! [X3: mworld,X5: mworld] : ( mrel @ X3 @ X5 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( big_p @ X6 @ X3 )
| ~ ( mrel @ ( esk4_1 @ X6 ) @ X3 )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,plain,
! [X3: mworld,X6: $i,X5: mworld] :
( ( eiw_di @ X6 @ X3 )
| ~ ( eiw_di @ X6 @ X5 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
thf(c_0_25,negated_conjecture,
! [X6: $i] :
( ( eiw_di @ ( esk3_1 @ X6 ) @ ( esk2_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_26,plain,
! [X26: mworld] : ( eiw_di @ ( esk1_1 @ X26 ) @ X26 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[eiw_di_nonempty])]) ).
thf(c_0_27,negated_conjecture,
! [X6: $i] :
( ~ ( big_p @ ( esk3_1 @ X6 ) @ ( esk6_1 @ X6 ) )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( big_p @ X6 @ X3 )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22])]) ).
thf(c_0_29,negated_conjecture,
! [X3: mworld,X6: $i] :
( ( eiw_di @ ( esk3_1 @ X6 ) @ X3 )
| ~ ( eiw_di @ X6 @ mactual ) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
thf(c_0_30,plain,
! [X3: mworld] : ( eiw_di @ ( esk1_1 @ X3 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_31,negated_conjecture,
! [X6: $i] :
~ ( eiw_di @ X6 @ mactual ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_32,plain,
! [X3: mworld,X5: mworld] : ( eiw_di @ ( esk1_1 @ X3 ) @ X5 ),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 % Computer : n007.cluster.edu
% 0.12/0.21 % Model : x86_64 x86_64
% 0.12/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.21 % Memory : 8046.5625MB
% 0.12/0.21 % OS : Linux 6.8.0-71-generic
% 0.12/0.21 % CPULimit : 300
% 0.12/0.21 % WCLimit : 300
% 0.12/0.21 % DateTime : Tue Sep 29 10:53:41 UTC 2026
% 0.12/0.21 % CPUTime :
% 0.12/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 Running higher-order theorem proving
% 0.25/0.31 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.9URpCxfZki/E---3.1_3205770.p
% 0.25/0.33 % Version: 3.5.1-ho
% 0.25/0.33 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.25/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.33 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.25/0.33 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.25/0.33 % Starting almost_fo_3_lam with 300s (1) cores
% 0.25/0.33 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.33 % ehoh_best2_full_lfho with pid 3205784 completed with status 0
% 0.25/0.33 % Result found by ehoh_best2_full_lfho
% 0.25/0.33 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.25/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.33 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.25/0.33 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.25/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.33 % No SInE strategy applied
% 0.25/0.33 % Search class: HHHNS-FFSF11-SHSSMFNN
% 0.25/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.33 % SubtermCWHack with pid 3205788 completed with status 0
% 0.25/0.33 % Result found by SubtermCWHack
% 0.25/0.33 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.25/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.33 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.25/0.33 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.25/0.33 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.33 % No SInE strategy applied
% 0.25/0.33 % Search class: HHHNS-FFSF11-SHSSMFNN
% 0.25/0.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.33 % Starting SubtermCWHack with 28s (1) cores
% 0.25/0.33 % Preprocessing time : 0.001 s
% 0.25/0.33
% 0.25/0.33 % Proof found!
% 0.25/0.33 % SZS status Theorem
% 0.25/0.33 % SZS output start CNFRefutation
% See solution above
% 0.25/0.34 % Parsed axioms : 30
% 0.25/0.34 % Removed by relevancy pruning/SinE : 0
% 0.25/0.34 % Initial clauses : 27
% 0.25/0.34 % Removed in clause preprocessing : 16
% 0.25/0.34 % Initial clauses in saturation : 11
% 0.25/0.34 % Processed clauses : 14
% 0.25/0.34 % ...of these trivial : 4
% 0.25/0.34 % ...subsumed : 0
% 0.25/0.34 % ...remaining for further processing : 10
% 0.25/0.34 % Other redundant clauses eliminated : 0
% 0.25/0.34 % Clauses deleted for lack of memory : 0
% 0.25/0.34 % Backward-subsumed : 5
% 0.25/0.34 % Backward-rewritten : 1
% 0.25/0.34 % Generated clauses : 6
% 0.25/0.34 % ...of the previous two non-redundant : 4
% 0.25/0.34 % ...aggressively subsumed : 0
% 0.25/0.34 % Contextual simplify-reflections : 1
% 0.25/0.34 % Paramodulations : 6
% 0.25/0.34 % Factorizations : 0
% 0.25/0.34 % NegExts : 0
% 0.25/0.34 % Equation resolutions : 0
% 0.25/0.34 % Disequality decompositions : 0
% 0.25/0.34 % Total rewrite steps : 8
% 0.25/0.34 % ...of those cached : 0
% 0.25/0.34 % Propositional unsat checks : 0
% 0.25/0.34 % Propositional check models : 0
% 0.25/0.34 % Propositional check unsatisfiable : 0
% 0.25/0.34 % Propositional clauses : 0
% 0.25/0.34 % Propositional clauses after purity: 0
% 0.25/0.34 % Propositional unsat core size : 0
% 0.25/0.34 % Propositional preprocessing time : 0.000
% 0.25/0.34 % Propositional encoding time : 0.000
% 0.25/0.34 % Propositional solver time : 0.000
% 0.25/0.34 % Success case prop preproc time : 0.000
% 0.25/0.34 % Success case prop encoding time : 0.000
% 0.25/0.34 % Success case prop solver time : 0.000
% 0.25/0.34 % Current number of processed clauses : 4
% 0.25/0.34 % Positive orientable unit clauses : 2
% 0.25/0.34 % Positive unorientable unit clauses: 0
% 0.25/0.34 % Negative unit clauses : 1
% 0.25/0.34 % Non-unit-clauses : 1
% 0.25/0.34 % Current number of unprocessed clauses: 1
% 0.25/0.34 % ...number of literals in the above : 2
% 0.25/0.34 % Current number of archived formulas : 0
% 0.25/0.34 % Current number of archived clauses : 6
% 0.25/0.34 % Clause-clause subsumption calls (NU) : 6
% 0.25/0.34 % Rec. Clause-clause subsumption calls : 6
% 0.25/0.34 % Non-unit clause-clause subsumptions : 2
% 0.25/0.34 % Unit Clause-clause subsumption calls : 4
% 0.25/0.34 % Rewrite failures with RHS unbound : 0
% 0.25/0.34 % BW rewrite match attempts : 1
% 0.25/0.34 % BW rewrite match successes : 1
% 0.25/0.34 % Condensation attempts : 0
% 0.25/0.34 % Condensation successes : 0
% 0.25/0.34 % Termbank termtop insertions : 1719
% 0.25/0.34 % Search garbage collected termcells : 496
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.005 s
% 0.25/0.34 % System time : 0.003 s
% 0.25/0.34 % Total time : 0.008 s
% 0.25/0.34 % Maximum resident set size: 3656 pages
% 0.25/0.34
% 0.25/0.34 % -------------------------------------------------
% 0.25/0.34 % User time : 0.008 s
% 0.25/0.34 % System time : 0.007 s
% 0.25/0.34 % Total time : 0.015 s
% 0.25/0.34 % Maximum resident set size: 4864 pages
% 0.25/0.34 % E exiting
%------------------------------------------------------------------------------